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Are all swans white? If we find one single black swan, logic allows us to conclude that the statement that all swans are white is false.

Falsifiability or refutability is the logical possibility that an assertion can be shown false by an observation or a physical experiment. That something is "falsifiable" does not mean it is false; rather, that if it is false, then this can be shown by observation or experiment. The term "testability" is related but more specific; it means that an assertion can be falsified through experimentation alone.

For example, "all men are mortal" is unfalsifiable, since no finite amount of observation could ever demonstrate its falsehood: that one or more men can live forever. "All men are immortal," by contrast, is falsifiable, by the presentation of just one dead man. Not all statements that are falsifiable in principle are falsifiable in practice. For example, "it will be raining here in one million years" is theoretically falsifiable, but not practically so.

Falsifiability is an important concept in science and the philosophy of science. The concept was made popular by Karl Popper, who, in his philosophical analysis of the scientific method, concluded that a hypothesis, proposition, or theory is "scientific" only if it is falsifiable. Popper asserted that unfalsifiable statements are non-scientific, but not of zero importance. For example, meta-physical or religious propositions have cultural or spiritual meaning, and the ancient metaphysical and unfalsifiable idea of the existence of atoms has led to corresponding falsifiable modern theories. A falsifiable theory that has withstood severe scientific testing is said to be corroborated by past experience, though in Popper's view this is not equivalent with confirmation and doesn't lead to the conclusion that the theory is true or even partially true.

Popper invented the notion of metaphysical research programs to name such ideas. In contrast to positivism, which held that statements are senseless if they cannot be verified or falsified, Popper claimed that falsifiability is merely a special case of the more general notion of criticizability, even though he admitted that refutation is one of the most effective methods by which theories can be criticized.

Naïve falsification

Two types of statements: observational and categorical

In work beginning in the 1930s, Popper gave falsifiability a renewed emphasis as a criterion of empirical statements in science.

Popper noticed that two types of statements are of particular value to scientists.

The first are statements of observations, such as "this is a white swan". Logicians call these statements singular existential statements, since they assert the existence of some particular thing. They can be parsed in the form: There is an x that is a swan, and x is white.

The second are statements that categorize all instances of something, such as "all swans are white". Logicians call these statements universal. They are usually parsed in the form: For all x, if x is a swan, then x is white. Scientific laws are commonly supposed to be of this type. One difficult question in the methodology of science is: How does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements?

Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from 'this is a white swan', 'that is a white swan', and so on, to a universal statement such as 'all swans are white'. This method is clearly deductively invalid, since it is always possible that there may be a non-white swan that has eluded observation (and, in fact, the discovery of the Australian black swan demonstrated the deductive invalidity of this particular statement).

Inductive categorical inference

Popper held that science could not be grounded on such an invalid inference. He proposed falsification as a solution to the problem of induction. Popper noticed that although a singular existential statement such as 'there is a white swan' cannot be used to affirm a universal statement, it can be used to show that one is false: the singular existential observation of a black swan serves to show that the universal statement 'all swans are white' is false—in logic this is called modus tollens. 'There is a black swan' implies 'there is a non-white swan,' which, in turn, implies 'there is something that is a swan and that is not white', hence 'all swans are white' is false, because that is the same as 'there is nothing that is a swan and that is not white'.

One notices a white swan. From this one can conclude:

At least one swan is white.

From this, one may wish to conjecture:

All swans are white.

It is impractical to observe all the swans in the world to verify that they are all white.

Even so, the statement all swans are white is testable by being falsifiable. For, if in testing many swans, the researcher finds a single black swan, then the statement all swans are white would be falsified by the counterexample of the single black swan.

Deductive falsification

Deductive falsification is different from an absence of verification. The falsification of statements occurs through modus tollens, via some observation. Suppose some universal statement U forbids some observationO:

Observation O, however, is made:

So by modus tollens,

Although the logic of naïve falsification is valid, it is rather limited. Nearly any statement can be made to fit the data, so long as one makes the requisite 'compensatory adjustments'. Popper drew attention to these limitations in The Logic of Scientific Discovery in response to criticism from Pierre Duhem. W. V. Quine expounded this argument in detail, calling it confirmation holism. In order to logically falsify a universal, one must find a true falsifying singular statement. But Popper pointed out that it is always possible to change the universal statement or the existential statement so that falsification does not occur. On hearing that a black swan has been observed in Australia, one might introduce the ad hoc hypothesis, 'all swans are white except those found in Australia'; or one might adopt another, more cynical view about some observers, 'Australian bird watchers are incompetent'.

Thus, naïve falsification ought to, but does not, supply a way of handling competing hypotheses for many subject controversies (for instance conspiracy theories and urban legends). People arguing that there is no support for such an observation may argue that there is nothing to see, that all is normal, or that the differences or appearances are too small to be statistically significant. On the other side are those who concede that an observation has occurred and that a universal statement has been falsified as a consequence. Therefore, naïve falsification does not enable scientists, who rely on objective criteria, to present a definitive falsification of universal statements.

Falsificationism

Naïve falsificationism is an unsuccessful attempt to prescribe a rationally unavoidable method for science. Sophisticated methodological falsification, on the other hand, is a prescription of a way in which scientists ought to behave as a matter of choice. The object of this is to arrive at an evolutionary process whereby theories become less bad.

Naïve falsification considers scientific statements individually. Scientific theories are formed from groups of these sorts of statements, and it is these groups that must be accepted or rejected by scientists. Scientific theories can always be defended by the addition of ad hoc hypotheses. As Popper put it, a decision is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it. At some point, the weight of the ad hoc hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it.

In place of naïve falsification, Popper envisioned science as evolving by the successive rejection of falsified theories, rather than falsified statements. Falsified theories are to be replaced by theories that can account for the phenomena that falsified the prior theory, that is, with greater explanatory power. For example, Aristotelian mechanics explained observations of everyday situations, but were falsified by Galileo’s experiments, and were replaced by Newtonian mechanics, which accounted for the phenomena noted by Galileo (and others). Newtonian mechanics' reach included the observed motion of the planets and the mechanics of gases. Or at least most of them; the size of the precession of the orbit of Mercury was not predicted by Newtonian mechanics, but was by Einstein's general relativity. The Youngian wave theory of light (i.e., waves carried by the luminiferous aether) replaced Newton's (and many of the Classical Greeks') particles of light but in turn was falsified by the Michelson-Morley experiment and was superseded by Maxwell's electrodynamics and Einstein's special relativity, which did account for the new phenomena. Furthermore, Newtonian mechanics applied to the atomic scale was replaced with Quantum Mechanics, when the old theory couldn't provide an answer to the Ultraviolet catastrophe, the Gibbs paradox, or how electron orbits could exist without the particles radiating away their energy and spiraling towards the centre. Thus the new theory had to posit the existence of unintuitive concepts such as Energy levels, Quanta and Heisenberg's Uncertainty Principle.

At each stage, experimental observation made a theory untenable (i.e., falsified it) and a new theory was found that had greater explanatory power (i.e., could account for the previously unexplained phenomena), and as a result, provided greater opportunity for its own falsification.

The criterion of demarcation

Popper uses falsification as a criterion of demarcation to draw a sharp line between those theories that are scientific and those that are unscientific. It is useful to know if a statement or theory is falsifiable, if for no other reason than that it provides us with an understanding of the ways in which one might assess the theory. One might at the least be saved from attempting to falsify a non-falsifiable theory, or come to see an unfalsifiable theory as unsupportable.

Popper claimed that, if a theory is falsifiable, then it is scientific.

The Popperian criterion excludes from the domain of science not unfalsifiable statements but only whole theories that contain no falsifiable statements; thus it leaves us with the Duhemian problem of what constitutes a 'whole theory' as well as the problem of what makes a statement 'meaningful'. Popper's own falsificationism, thus, is not only an alternative to verificationism, it is also an acknowledgement of the conceptual distinction that previous theories had ignored.

Popper noticed that the philosophers of the Vienna Circle had mixed two different problems, that of meaning and that of demarcation, and had proposed in verificationism a single solution to both. In opposition to this view, Popper emphasized that there are meaningful theories that are not scientific, and that, accordingly, a criterion of meaningfulness does not coincide with a criterion of demarcation. Verifiability came to be replaced by falsifiability as the criterion of demarcation.

Use in courts of law

Falsifiability was one of the criteria used by Judge William Overton in the McLean v. Arkansas ruling to determine that 'creation science' was not scientific and should not be taught in Arkansaspublic schools. In his conclusion related to this criterion he stated that "While anybody is free to approach a scientific inquiry in any fashion they choose, they cannot properly describe the methodology as scientific, if they start with the conclusion and refuse to change it regardless of the evidence developed during the course of the investigation."[2]

Criticisms

Contemporary philosophers

Many contemporary philosophers of science and analytic philosophers are strongly critical of Popper's philosophy of science. Popper's mistrust of inductive reasoning has led to claims that he misrepresents scientific practice. Among the professional philosophers of science, the Popperian view has never been seriously preferred to probabilistic induction, which is the mainstream account of scientific reasoning.[3] Adherents of Popper speak with disrespect of "professional philosophy", for example W. W. Bartley:

Sir Karl Popper is not really a participant in the contemporary professional philosophical dialogue; quite the contrary, he has ruined that dialogue. If he is on the right track, then the majority of professional philosophers the world over have wasted or are wasting their intellectual careers. The gulf between Popper's way of doing philosophy and that of the bulk of contemporary professional philosophers is as great as that between astronomy and astrology.[4]

Rafe Champion:

Popper's ideas have failed to convince the majority of professional philosophers because his theory of conjectural knowledge does not even pretend to provide positively justified foundations of belief. Nobody else does better, but they keep trying, like chemists still in search of the Philosopher's Stone or physicists trying to build perpetual motion machines.[5]

and David Miller:

‘What distinguishes science from all other human endeavours is that the accounts of the world that our best, mature sciences deliver are strongly supported by evidence and this evidence gives us the strongest reason to believe them.’ That anyway is what is said at the beginning of the advertisement for a recent conference on induction at a celebrated seat of learning in the UK. It shows how much critical rationalists still have to do to make known the message of Logik der Forschung concerning what empirical evidence is able to do and what it does.[6]

Kuhn and Lakatos

Whereas Popper was concerned in the main with the logic of science, Thomas Kuhn’s influential book The Structure of Scientific Revolutions examined in detail the history of science. Kuhn argued that scientists work within a conceptual paradigm that strongly influences the way in which they see data. Scientists will go to great length to defend their paradigm against falsification, by the addition of ad hoc hypotheses to existing theories. Changing a 'paradigm' is difficult, as it requires an individual scientist to break with his or her peers and defend a heterodox theory.

Some falsificationists saw Kuhn’s work as a vindication, since it provided historical evidence that science progressed by rejecting inadequate theories, and that it is the decision, on the part of the scientist, to accept or reject a theory that is the crucial element of falsificationism. Foremost amongst these was Imre Lakatos.

Lakatos attempted to explain Kuhn’s work by arguing that science progresses by the falsification of research programs rather than the more specific universal statements of naïve falsification. In Lakatos' approach, a scientist works within a research program that corresponds roughly with Kuhn's 'paradigm'. Whereas Popper rejected the use of ad hoc hypotheses as unscientific, Lakatos accepted their place in the development of new theories.

Some philosophers of science, such as Paul Feyerabend, take Kuhn's work as showing that social factors, rather than adherence to a purely rational method, decide which scientific theories gain general acceptance. Many other philosophers of science dispute such a view, such as Alan Sokal and Kuhn himself.

Feyerabend

Paul Feyerabend examined the history of science with a more critical eye, and ultimately rejected any prescriptive methodology at all. He rejected Lakatos’ argument for ad hoc hypothesis, arguing that science would not have progressed without making use of any and all available methods to support new theories. He rejected any reliance on a scientific method, along with any special authority for science that might derive from such a method. Rather, he claimed that if one is keen to have a universally valid methodological rule, epistemological anarchism or anything goes would be the only candidate. For Feyerabend, any special status that science might have derives from the social and physical value of the results of science rather than its method.

Sokal and Bricmont

In their book Fashionable Nonsense (published in the UK as Intellectual Impostures) the physicists Alan Sokal and Jean Bricmont criticized falsifiability on the grounds that it does not accurately describe the way science really works. They argue that theories are used because of their successes, not because of the failures of other theories. Their discussion of Popper, falsifiability and the philosophy of science comes in a chapter entitled "Intermezzo," which contains an attempt to make clear their own views of what constitutes truth, in contrast with the extreme epistemological relativism of postmodernism.

Sokal and Bricmont write, "When a theory successfully withstands an attempt at falsification, a scientist will, quite naturally, consider the theory to be partially confirmed and will accord it a greater likelihood or a higher subjective probability. ... But Popper will have none of this: throughout his life he was a stubborn opponent of any idea of 'confirmation' of a theory, or even of its 'probability'. ... [but] the history of science teaches us that scientific theories come to be accepted above all because of their successes." (Sokal and Bricmont 1997, 62f)

They further argue that falsifiability cannot distinguish between astrology and astronomy, as both make technical predictions that are sometimes incorrect.

David Miller, a contemporary philosopher of critical rationalism, has attempted to defend Popper against these claims.[7]

Examples

Claims about verifiability and falsifiability have been used to criticize various controversial views. Examining these examples shows the usefulness of falsifiability by showing us where to look when attempting to criticise a theory.

Non-falsifiable theories can usually be reduced to a simple uncircumscribed existential statement, such as there exists a green swan. It is entirely possible to verify whether or not this statement is true, simply by producing the green swan. But since this statement does not specify when or where the green swan exists; it is simply not possible to show that the swan does not exist, and so it is impossible to falsify the statement.

That such theories are unfalsifiable says nothing about either their validity or truth. But it does assist us in determining to what extent such statements might be evaluated. If evidence cannot be presented to support a case, and yet the case cannot be shown to be indeed false, not much credence can be given to such a statement. However, you can also look at this case from another perspective. Let's say that the statement is "all swans are not green". An attempt to verify this positively would require a search for non-green swans, which you are sure to find. However, having rounded up and examined every known swan, there is always the possibility that there is at least one more swan but we will never know for sure until we find it and if we do, there may be yet, one more swan, and it may be green. On the other hand, we may say that "all swans are not green" but instead of attempting to positively verify this statement we attempt to falsify it by looking for a green swan. In that case, we need only find one swan (a green one), in the absence of which we can accept the original statement as a working hypothesis until such a swan is discovered.

Economics

The most common argument is made against rational expectations theories, which work under the assumption that people act to maximize their utility. However, under this viewpoint, it is impossible to disprove the fundamental theory that people are utility-maximizers. The political scientistGraham T. Allison, in his book Essence of Decision, attempted to both quash this theory and substitute other possible models of behavior.

Ethics

Ethical statements such as "murder is evil" or "it is good to help those in need" are not usually considered to be falsifiable. This does not necessarily amount to conclusion that they are all false, or without truth-values. It mainly affects their status as scientific theories. The meta-ethical thesis that ethical statements have no truth-value is called non-cognitivism.

Evolution

If it were possible by direct means to determine the lack of a common ancestor, it would involve proving a negative. As a result, it would be logically invalid to observe an act directly falsifying the existence of a common ancestor, just as it would be impossible to falsify the existence of an invisible God. Numerous examples of potential (indirect) ways to falsify common descent have been proposed amongst evolutionists. Richard Dawkins said that "If there were a single hippo or rabbit in the Precambrian, that would completely blow evolution out of the water. None have ever been found."[9][10][11] This is an elaboration of the original quote from J.B.S. Haldane who, when asked what hypothetical evidence could disprove evolution, replied "fossil rabbits in the Precambrian era".[12]

Popper himself drew a distinction between common descent and the process of natural selection. While he agreed with evolutionists that common descent was falsifiable (he used the even more drastic example of the remains of a car in cambrian sediments),[13] he argued against them when he said that natural selection "is not a testable scientific theory but a metaphysical research programme".[14]

Popper later recanted, "I have changed my mind about the testability and logical status of the theory of natural selection, and I am glad to have the opportunity to make a recantation."[15] He went on to formulate natural selection in a falsifiable way and offered a more nuanced view of its status. He still felt that "Darwin's own most important contribution to the theory of evolution, his theory of natural selection, is difficult to test." However, "[t]here are some tests, even some experimental tests; and in some cases, such as the famous phenomenon known as 'industrial melanism', we can observe natural selection happening under our very eyes, as it were.[15]

Historicism

Theories of history or politics which allegedly predict the future course of history have a logical form that renders them neither falsifiable nor verifiable. They claim that for every historically significant event, there exists an historical or economic law that determines the way in which events proceeded. Failure to identify the law does not mean that it does not exist, yet an event that satisfies the law does not prove the general case. Evaluation of such claims is at best difficult. On this basis, Popper himself argued that neither Marxism nor psychoanalysis was science, although both made such claims. Again, this does not mean that any of these types of theories is necessarily incorrect. Popper considered falsifiability a test of whether theories are scientific, not of whether propositions that they contain or support are true.

Advocates of historicism (particularly advocates of historical materialism) would suggest that their theory would be decisively refuted if modern capitalist society as a whole decided to restore monarchy and its feudalist forms of production. Except in catastrophic circumstances, such "random" shifts in social organization are considered impossible by historical materialists and most historicists - thus demonstrating a clear scientific falsifiability.

Logic and mathematics

The question may be raised as to whether the theorems of logic and mathematics are falsifiable or not. After all, it is self-evident that they are unexceptionally true. In considering this question, it is helpful to introduce a classical distinction that is frequently emphasized in this connection by Charles Sanders Peirce. On the one hand, he defines a positive science as "an inquiry which seeks for positive knowledge", that is, for knowledge that can be expressed in a categorical proposition (Peirce, The Essential Peirce (EP) v. 2, 144). He goes on to say the following of the normative sciences, namely, logic, ethics and aesthetics:

Logic and the other normative framework ask not what is but what ought to be. They are nevertheless positive sciences since it is by asserting positive, categorical truth that they are able show that what really is so; and the right reason derived from positive categorical fact. (Peirce, EP 2, 144).

On the other hand, Peirce distinguishes mathematics proper from all positive sciences, and reckons it more fundamental than any of them, saying that any positive science "must, if it is to be properly grounded, be made to depend upon the Conditional or Hypothetical Science of Pure Mathematics, whose only aim is to discover not how things actually are, but how they might be supposed to be, if not in our universe, then in some other" (Peirce, EP 2, 144).

In this way of looking at things, logic is a science that seeks after knowledge of how we ought to conduct our reasoning if we want to achieve the goals of reasoning. As such, the logical knowledge that we have at any given time can easily fall short of perfection. However, the laws of logic themselves (the rules of inference and logical axioms) are not subject to falsifiability per se. That is, since truth values are defined in relation to the laws of logic any "falsification" of these laws would represent a self-contradictory situation though this conclusion has been argued against by philosophers such as W.V. Quine.

Pure mathematics, on the contrary, contains no propositions that are not contingent on prior assumptions. Its apparent certainty is but a relative certainty, relative to the certainty of its axioms. One can say that its theorems are tautologies, so long as one remembers the original meaning of tautology, which is a repetition of something previously asserted. Mathematical theorems merely say more acutely what the axioms more obtusely already say.

Applied mathematics, in particular, mathematics as applied in empirical science, is still more generalized. The application of mathematical abstractions to a domain of experiential phenomena involves a critical comparison of many different mathematical models, not all of them consistent with each other, and it normally leads to a judgment that some of the hypothetical models are better analogues or more likely icons than others of the empirical domain in question. This is, of course, an extremely fallible business, and each judgment call is subject to revision as more empirical data comes in.

How well a mathematical formula applies to the physical world is a physical question, and thus testable, within certain limits. For example, the proposition that all objects follow a parabolic path when thrown into the air is falsifiable; indeed, it is false. To see this, one has but to think of a feather. A slightly better proposition is that all objects follow a parabolic path when thrown in a vacuum and acted upon by gravity, which is itself falsified in regard to paths whose lengths are not negligible in proportion to a given planet's radius.

What is the conclusion then? Are mathematical theorems falsifiable or not? The most that can be said of them is that they are true of what they are true of, but what they are true of may not be the object of a given experience.

The above discussion addressed the nature of mathematical theorems in and of themselves, and then took up their application to empirical phenomena. But the actual practice of mathematics involves yet another level of consideration, and it may yet involve activities that are very similar to empirical science. Many working mathematicians, from Peirce in his day to Stephen Wolfram in ours, have remarked on the active, observational, and even experimental character of mathematical work. Imre Lakatos brings the concept of falsifiability to bear on the discipline of mathematics in his Proofs and Refutations. The question of whether mathematical practice is a quasi-experimental science depends in part on whether proofs are fundamentally different from experiments. Lakatos argues that often axioms, definitions, and proofs evolve through criticism and counterexample in a manner not unlike the way that a scientific theory evolves in response to experiments.

Solipsism

Metaphysical solipsism is the view that the individual self of the solipsistic philosopher is the whole of reality and that the external world and other persons are representations of that self having no independent existence (Wood, p. 295). Metaphysical solipsism is not empirically falsifiable because once one has taken the solipsistic position, any evidence that might establish an external world is already viewed as being within (or produced by) the self. However, expressions of solipsism may be self-refuting.

Anti-solipsism—the position that an external world does exist—is similarly non-falsifiable because regardless of what evidence is produced, it is always possible that there exists an external world outside one's experiences that does not interact with them.

Theism

The idea of falsifiability can be used to draw a distinction between falsifiable and nonfalsifiable notions of a god. The nonfalsifiable notions describe what we think of as a god's transcendental qualities; because they are independent of anything in the physical world, no physical circumstances are sufficient to prove or disprove their existence. By contrast, falsifiable accounts of a god are physically definite, and can therefore be thought of as a personification, or "deification," of ideas that, at least purportedly, could be formulated as (read: testable) theories of physics.[citation needed]

Quotations

No amount of experimentation can ever prove me right; a single experiment can prove me wrong. — Albert Einstein[16]

The criterion of the scientific status of a theory is its falsifiability, or refutability, or testability. — Karl Popper, (Popper, CR, 36)

Scientists make hypotheses and theories about their fields of study. At the start, they hope their hypothesis or theory is true but they and other scientists will use the scientific method to try and prove it false. Falsifiability (or refutability) means that an example can be found through an experiment or an observation where the hypothesis is wrong.

This can mean one of the following:

The theory does not apply to the example

The theory can be proved wrong (for this example)

Put another way, if a scientist comes up with a rule or law (such as gravity), they have to also be able to imagine a way to show that it is wrong.

Karl Popper had the opinion that only theories that are falsifiable are scientific.

Example

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Crow is a generic term for about 40 different kinds of birds. It would be possible to make a theory All crows are white. The sentence All crows are white can also be written as There are no crows that are non-white. If someone observes a black crow, he could say There are black crows (alternatively: There is at least one crow that is black). This is a contradiction to All crows are white, and falsifies the theory.

Problems

There are some problems:

Kurt Gödel has shown that certain propositions inside a system of logic cannot be proved inside that system.

Closely related to this is the fact that some statements are undecidable (This statement is false, see paradox). Undecidable statements cannot be falsified